Question 2 Function Notations: Tell whether the relationships of N and M shown in the table below is a function or not. If it is a function which variable is the input and which is the output variable and why? (Give reasons for both answers) N 1 0 1 0 8 M -3 2 -3 2 1 Both N and M can be functions since there are only one value for the output variable when the input variables are the same, e.g. N(0) = 2 and N(1) = -3 also M(2) = 0 and M(-3) = 1.

Question 2 - Find the slope of the function between (a) x = -2 and -1 and (b) x =1 and x = 2 x f(x) slope -2 -8 -1 -1 1 1 2 8 Note the shape of the function between both domains.

Question 3 - Geometric Properties of Linear Functions Write a formula for the line in the form y = mx + b that is perpendicular to y = ¼ x +1 and passes through the point P(-1, 4). So (y - 4) = -4(x + 1)  gives y = -4x + 0 Ans:

Question 3 - Formula for Linear Function Write a possible formula for the linear depreciation of the value of a car from $25,500 in 1984 to $12,500 in 2001. Let t = 0 be 1984, so V0 = 25,500 , m  = (12500 - 25500)/(2001-1984) V = -764.71t + 25500

Question 4 - Composition of Functions Given (a) What is (b) What is h(1)? (a) (b)

Question 4 - Composite If and what is Ans: So g(1) = 9

Question 5 - Domain and range What is the domain and range of the function: ? Ans: Domain x cannot be -2 (division by 0) and y cannot be 3 since 1/(x+2) never gets to be equal to zero; however y, the range can be positive and negative. Domain: Range:

Question 5 - Domain and Range What is the domain and range of the function ? Domain:   (sqrt cannot contain a real negative number) Range    (smallest y is when sqrt = 0, 3 and largest y is when x = 0 or y = 5 + 3 = 8)

Question 6 - Piecewise function (a) Sketch the piecewise function f(x) = and (b) What is x when f(x) = 4? Ans x = -3 (equation (1))

Question 6 - Piecewise Function For the piecewise defined function what is the value of x when f(x) = 1? f(x) = - Function is undefined for x when f(x) =1 (will give partial credits if skecth graph)

Question 7 - Inverse functions Write the inverse function of . Ans

Question 7 - Inverse What is the inverse of the function?

Question 8 - Intersections of Linear functions. When will these two linear functions be equal to each other? (1) 4x + 5y = -8 and (2) 3x + y = 5 When (x, y) = (3, -4) Note:  solve for y in both first and set equal to each other, then solve for x  and use x to find y.

Question 8 - Intersections of Linear functions. When will these two linear functions be equal to each other? (1) 2x - 7y = 4 and (2) 3y - x = 1 Ans: (-19, -6)

Question 9 - Quadratic Find the zeros of the function Ans: Quadratic formula About -2.4641 and 4.4641

Question 9 - Quadratic Find the roots of the quadratic function ; if none exist state why. Set y = 0 and multiply by -2, then factor out x to get x(x - 3) = 0 or use quadratic equation  Roots are x = 0 and 3

Question 10 - 3.1 Quadratic What is the vertex of the quadratic formula ? Ans: (h, k) = ) or solve by completing the square. (h, k) = (-7.5, 24.75)

Question 10 - Quadratic If the height (feet) of an object above the ground is given t seconds after it is launched is given by the quadratic formula. H(t) = -16t2 + 48t, when will the object be at its maximum height? (hint: find the t coordinate of the vertex) Vertex is (1.5, 36) or 1.5 seconds after it is launched.

Question 11 - 3.1 Exponential Growth If the concentration of alcohol in 25 year old Michael's body t hours after drinking 4 glasses of his favorite drink is given by the formula A(t) = 0.15(1-r)t and the rate of dissipation of the alcohol each hour is 25%. (a) What is amount of alcohol in the body after 6 ½ hour? (b) What does the 0.15 represent? Ans (a) (b) 0.15 is the initial concentration of alcohol in Michael's body after he is finish drinking the 4 glasses.

Question 11  Concavity Calculate successive rates of change for the functions, H(t) in the table below and decide whether the graph is concave up or concave down. x 2 5 8 11 H(x) 11.3 13.32 14.98 16.12 rate  = 0.6733 rate  = 0.5533 rate  =  0.38 The rate of change is decreasing so concave down